TIME FRACTIONAL ADVECTION-DISPERSION EQUATION

  • Liu, F. (Department of Mathematics, Xiamen University) ;
  • Anh, V.V. (School of Mathematical Sciences, Queensland University of Technology) ;
  • Turner, I. (School of Mathematical Sciences, Queensland University of Technology) ;
  • Zhuang, P. (Department of Mathematics, Xiamen University)
  • 발행 : 2003.09.01

초록

A time fractional advection-dispersion equation is Obtained from the standard advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order ${\alpha}$(0 < ${\alpha}$ $\leq$ 1). Using variable transformation, Mellin and Laplace transforms, and properties of H-functions, we derive the complete solution of this time fractional advection-dispersion equation.

키워드

참고문헌

  1. Adv. Appl. Prob. v.32 Fractional diffusion and fractional heat equation J.M.Angulo;M.D.Ruiz-Medina;V.V.Anh;W.Grecksch
  2. Statistics and Probability Letters v.48 Scaling laws for fractional diffusion-wave equations with singular data V.V.Anh;N.N.Leonenko
  3. J. Statist. Phys. v.104 Spectral analysis of fractional kinetic equations with random data V.V.Anh;N.N.Leonenko
  4. J. Appl. Math. and Computing v.10 On quadratic fractional generalized solid bi-criterion M.Basu;D.P.Acharya
  5. Water Resour. Res. v.36 no.6 Application of a fractional advection-despersion equation D.A.Benson;S.W.Wheatcraft;M.M.Meerschaert
  6. Water Resour. Res. v.36 no.6 The fractional-order governing equation of Levy motion D.A.Benson;S.W.Wheatcraft;M.M.Meerschaert
  7. Fractal Burgers equation v.147 Ⅰ. Differential Equations P.Biler;T.Funaki;W.A.Woyczynski
  8. Rend. Fis. Acc. Lincei(ser. 9) v.7 The Green function of the diffusion of fluids in porous media with memory M.Caputo
  9. Korean J. Comput. Appl. Math. v.9 Continuation theorem of fractionalorder evolutionary integral equations A.M.A.El-Sayed;M.A.E.Aly
  10. Tables of Integral Transforms v.1 A.Erdelyi
  11. Chem. Eng. J. v.bf49 A theory of transport phenomena in disordered systems R.Giona;H.E.Roman
  12. Fractional Calculus Appl. Anal. v.2 Analytical properties and applications of the Wright function R.Gorenflo;Yu.Luchko;F.Mainardi
  13. J. Comp. Appl. Math. v.118 Wright function as scale-invariant solutions of the diffusion-wave equation R.Gorenflo;Yu.Luchko;F.Mainardi
  14. Fractals v.3 Exact solutions for a class of fractal time random walks R.Hilfer
  15. Proceedigns of the International Conference on Boundary and Interior Layers Numerical solution of the fractional-order advection-dispersion equation F.Liu;V.Anh;I.Turner
  16. Waves and Stability in Continuous Media On the initial value problem for the fractional diffusion-wave equation F.Mainardi;S.Rionero(Ed.);T.Ruggeri(Ed.)
  17. IUTAM Symposium - Nonlinear Waves in Solids Fractional diffusive waves in viscoelastic solids F.Mainardi;J.L.Wagner(Ed.);F.R.Norwood(Ed.)
  18. Fractional Calculus Appl. Anal. v.4 The fundamental solution of the space-time fractional diffusion equation F.Mainardi;Yu.Luchko;G.Pagnini
  19. An Introduction to the Fractional Calculus and Fractional Differential Equations K.S.Miller;B.Ross
  20. The Fractional Calculus K.B.Oldham;J.Spanier
  21. Fractional Differential Equations I.Podlubny
  22. Chaos v.7 Fractional kinetic equations: solutions and applications A.Saichev;G.Zaslavsky
  23. Fractional Integrals and Derivatives: Theory and Applications v.30 S.G.Samko;A.A.kilbas;O.I.Marichev
  24. J. Math. Phys. v.30 Fractional diffusion and wave equations W.R.Schneider;W.Wyss
  25. J. Math. Phys. v.27 The fractional diffusion equation W.Wyss
  26. Fractional Calculus Appl. Anal. v.3 The fractional Black-Scholes equation W.Wyss